This study presents a methodology for optimal control of connected automated vehicles (CAVs) in freeway segments with a lane drop. Lane drops can create bottlenecks with a considerable number of mandatory and discretionary lane-changing maneuvers when traffic volume is high, which can eventually lead to stop-and-go conditions. Proper motion planning aligned with optimal lane changing upstream of a lane drop can increase capacity and reduce the number of stops and the risk of collision. This paper introduces a vehicle-level mixed-integer program to control longitudinal and lateral movement of CAVs, provide a smooth flow of traffic, and avoid congestion in freeway segments with lane drops. To ensure the feasibility of vehicle-level decisions and promote system-level optimality, a cooperative distributed algorithm is established, where CAVs coordinate their decisions to find the optimal longitudinal and lateral maneuvers that avoid collisions among all vehicles. The proposed coordination scheme lets CAVs find their optimal trajectories based on predictive information from surrounding vehicles (i.e., future locations and speeds) and coordinate their lane-changing decisions to avoid collisions. The results show that optimal lane changing of CAVs smoothens the traffic flow and increases freeway capacity in congested traffic conditions. Compared with all-knowing CAVs simulated in Vissim, the proposed methodology reduced the average travel time by up to 86.4%. It increased the number of completed trips by up to 134.3% based on various traffic demands and lane drop layout combinations.